KYIV, Ukraine (AP) - Ukraine said it saw possible room for compromise in talks with Russia despite Moscow's stepped up bombardment Tuesday of Kyiv and new assaults on the port city of Mariupol, from where an estimated 20,000 civilians managed to flee through a humanitarian corridor.

The fast-moving developments on the diplomatic front and on the ground came as Russia's invasion neared the three-week mark and the number of Ukrainians who have left the country amid Europe's heaviest fighting since World War II eclipsed 3 million.

After delegations from Ukraine and Russia met again Tuesday via video, Ukrainian President Volodymyr Zelenskyy said early Wednesday that Russia’s demands were becoming “more realistic." The two sides were expected to speak again Wednesday.

“Efforts are still needed, patience is needed,” he said in his nightly video address to the nation. “Any war ends with an agreement.”

Zelenskyy, who was expected to address the U.S. Congress on Wednesday, thanked President Joe Biden and “all the friends of Ukraine” for $13.6 billion in new support.

He appealed for more weapons and more sanctions to punish Russia, and repeated his call to “close the skies over Ukraine to Russian missiles and planes.”

He said Russian forces on Tuesday had been unable to move deeper into Ukrainian territory but had continued their heavy shelling of cities.

Over the past day, 28,893 civilians were able to flee the fighting through nine humanitarian corridors, although the Russians refused to allow aid into Mariupol, he said.

In other developments, the leaders of three European Union countries - Poland, the Czech Republic and Slovenia - visited the embattled capital Tuesday, arriving by train in a bold show of support amid the danger.

Meanwhile, large explosions thundered across Kyiv before dawn from what Ukrainian authorities said were artillery strikes, as Russia’s bombardment of the capital appeared to become more systematic and edged closer to the city center, smashing apartments, a subway station and other civilian sites.

Zelenskyy said Tuesday that barrages hit four multi-story buildings in the city and killed dozens. The strikes disrupted the relative calm that returned after an initial advance by Moscow's forces was stopped in the early days of the war.

A senior U.S. defense official, speaking on the condition of anonymity to discuss the Pentagon's assessment, said that the Russians were using long-range fire to hit civilian targets inside Kyiv with increasing frequency but that their ground forces were making little to no progress around the country. The official said Russian troops were still about 15 kilometers (9 miles) from the center of the capital.

The official said the U.S. has seen indications that Russia believes it may need more troops or supplies than it has on hand in Ukraine, and it is considering ways to get more resources into the country. The official did not elaborate.

Before Tuesday's talks, Russian Foreign Minister Sergey Lavrov said Moscow would press its demands that Ukraine drop its bid to join NATO, adopt a neutral status and “demilitarize.”

In a statement that seemed to signal potential grounds for agreement with Moscow, Zelenskyy told European leaders gathered in London that he realizes NATO has no intention of accepting Ukraine.

“We have heard for many years about the open doors, but we also heard that we can’t enter those doors,” he said. “This is the truth, and we have simply to accept it as it is.”

NATO does not admit nations with unsettled territorial conflicts. Zelenskyy has repeatedly said in recent weeks that he realizes NATO isn’t going to offer membership to Ukraine and that he could consider a neutral status for his country but needs strong security guarantees from both the West and Russia.

The U.N. said close to 700 civilians in Ukraine have been confirmed killed, with the true figure probably much higher.

Two journalists working for Fox News were killed when the vehicle they were traveling in was hit by fire Monday on the outskirts of Kyiv, the network said. Fox identified the two as video journalist Pierre Zakrzewski and Ukrainian journalist Oleksandra “Sasha” Kuvshynova, who was helping Fox crews navigate the area. Another journalist was killed Sunday in Ukraine.

New efforts to bring civilians to safety and deliver aid were underway around the country. The Red Cross said it was working to evacuate people in about 70 buses from the northeastern town of Sumy, near the Russian border.

The exodus from Mariupol marked the biggest evacuation yet from the southern city of 430,000, where officials say a weekslong siege has killed more than 2,300 people and left residents struggling for food, water, heat and medicine. Bodies have been buried in mass graves.

Kyrylo Tymoshenko, a senior aide to Zelenskyy, said that about 20,000 people managed to leave Mariupol on Tuesday in 4,000 private vehicles via a designated safe corridor leading to the city of Zaporizhzhia.

On a day when thousands managed to leave Mariupol, Russian troops seized the city's largest hospital, said regional leader Pavlo Kyrylenko. He said the troops forced about 400 people from nearby homes into the Regional Intensive Care Hospital and were using them and roughly 100 patients and staff as human shields by not allowing them to leave.

Kyrylenko said shelling had already heavily damaged the hospital's main building, but medical staff have been treating patients in makeshift wards in the basement.

Doctors from other Mariupol hospitals made a video to tell the world about the horrors they've been seeing. “We don’t want to be heroes and martyrs posthumously,” one woman said. She also said it's insufficient to simply refer to people as the wounded: "it’s torn off arms and legs, gouged out eyes, bodies torn into fragments, insides falling out.”

Meanwhile, the Ukrainian army’s general staff said Tuesday evening that Russian troops had launched another assault on the strategically important city.

Fighting has intensified on Kyiv's outskirts in recent days, and air raid sirens wailed inside the capital. The mayor imposed a curfew extending through Thursday morning.

Tuesday's artillery strikes hit the Svyatoshynskyi district of western Kyiv, adjacent to the suburb of Irpin, which has seen some of the worst fighting of the war.

Flames shot out of a 15-story apartment building and smoke choked the air as firefighters climbed ladders to rescue people. The assault blackened several floors of the building, ripped a hole in the ground outside and blew out windows in neighboring apartment blocks. Rescue workers said at least one person was killed.

“Yesterday we extinguished one fire, today another. It is very difficult,” a firefighter who gave only his first name, Andriy, said outside the building, tears falling from his eyes. “People are dying, and the worst thing is that children are dying. They haven’t lived their lives and they have already seen this."

City authorities also tweeted an image of the blown-out facade of a downtown subway station that had been used as a bomb shelter and said trains would no longer stop at the station.

A 10-story apartment building in the Podilsky district of Kyiv, north of the government quarter, was damaged. Russian forces also stepped up strikes overnight on Irpin and the northwest Kyiv suburbs of Hostomel and Bucha, said the head of the capital region, Oleksiy Kuleba.

“Many streets have been turned into a mush of steel and concrete. People have been hiding for weeks in basements, and are afraid to go out even for evacuations,” Kuleba said on Ukrainian television.

In the country's east, Russian forces launched more than 60 strikes overnight Monday into Tuesday on Ukraine’s second-largest city, Kharkiv, according to regional administration chief, Oleh Sinehubov. The strikes hit the city’s historical center, including the main marketplace.

He said the bodies of dozens of civilians were pulled from destroyed apartment buildings.

On Tuesday evening, Ukrainian forces repelled Russian troops who tried to storm Ukraine's second-largest city, Kharkiv, from their positions in Piatykhatky, a suburb 15 kilometers (9 miles) to the north, the regional administration chief, Oleh Sinehubov, said on Telegram. He said the Kharkiv's defenders were able “to push the enemy back beyond its previous position,” in what he described as a “shameful defeat” for Russia.

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Associated Press writers Lolita C. Baldor in Washington, Raf Casert in Brussels and AP journalists from around the world contributed to this report.